On penetration depth of typical earth-penetrating projectilesinto concrete targets considering the scaling effect
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摘要: 准确评估精确制导武器的侵彻深度可为防护工程设计提供重要参考。已有研究工作大多集中于中、小口径弹体和普通强度混凝土靶体，且由于尺寸效应的影响使得现有计算方法对预测大口径典型钻地弹侵彻深度的适用性值得商榷。首先，综合分析了已有弹体侵彻试验数据，发现引起侵彻深度尺寸效应的主要原因是混凝土粗骨料粒径未随弹体尺寸进行同比缩放；其次，开展了5发100.0和203.0 mm口径缩比钻地弹侵彻C40和C100混凝土的试验和数值模拟分析，提出并验证了大口径弹体侵彻混凝土深度的实用化有限元计算方法；然后，确定了美军5种典型钻地弹在不同侵彻速度（100~600 m/s）下对上述2种强度混凝土靶体的侵彻深度，并对现有7种计算公式的适用性进行了评估；最后，基于已有大量试验数据拟合确定了侵彻深度随混凝土强度的衰减规律，并计算得到340 m/s侵彻速度下5种典型钻地弹对C40~C200混凝土的侵彻深度。Abstract: Accurately evaluating the penetration depth of precision-guided weapons can provide an important reference for the design of protective engineering. The existing work mainly focuses on small or medium caliber projectiles and normal strength concrete targets. Besides, the applicability of existing calculation methods to predict the penetration depth of typical large-caliber earth-penetrating projectiles is worthy of discussion due to the scaling effect. Firstly, by analyzing the existing penetration test data, the main cause of the size effect of penetration depth is that the particle size of the coarse aggregate is not scaled with the projectile size accordingly. Then, five tests were carried out with 100.0-mm and 203.0-mm caliber scaled earth-penetrating projectiles penetrating into C40 and C100 concrete targets. The corresponding two-dimensional axisymmetric finite element model was established. By adjusting the predefined value of the eroding plastic strain to make the numerical penetration depth close to the test data, the constitutive model parameters, as well as the matched mesh size and the erosion criterion, were determined. Thus, a practical finite element analyses method for the penetration depth of large-caliber projectiles into concrete was proposed and verified. Furthermore, for the above two concrete strength grades, the penetration depths of the five typical earth-penetrating projectiles of the U.S. military into concrete at different impact velocities (100－600 m/s) were determined, and the applicability of the existing seven empirical or semi-empirical formulas was evaluated. The comparison results show that the ACE formula can obtain a better prediction of the penetration depth. Finally, the attenuation law of the penetration depth with the compressive strength of concrete was confirmed by fitting the existing penetration test data. The corresponding penetration depths of the five typical earth-penetrating projectiles into the C40－C200 concrete targets at the velocity of 340 m/s were determined. The present work and conclusions can be directly used in the protective engineering design.
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Key words:
- concrete target /
- penetration depth /
- earth-penetrating projectile /
- scaling effect
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图 11 C40混凝土中5种战斗部的无量纲侵彻深度
Figure 11. Non-dimensional penetration depths of five warheads into C40 concrete
图 12 C100混凝土中5种战斗部无量纲侵彻深度
Figure 12. Non-dimensional penetration depths of five warheads into C100 concrete
图 13 Kq与
$ {f'_{\text{c}}} $ 之间的关系Figure 13. Relationship between Kq and
$ {f'_{\text{c}}} $ 
图 14 不同混凝土强度等级下5种战斗部的侵彻深度
Figure 14. Penetration depths of five warheads into the concrete of different strengths
表 1 试验结果
Table 1. Test results
试验编号 f/MPa d/mm M/kg v0/（m·s−1） P/m 1 40 100.0 17.3 503 0.86 2 40 105.0 20.1 325 0.52 3 100 100.0 17.3 357 0.35 4 100 100.0 17.3 510 0.51 5 100 203.0 145.0 360 0.87 
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表 2 5种战斗部参数
Table 2. Parameters of five warheads
战斗部 d/mm M/kg L/mm w/mm ψ BLU-109B 368.3 874 2 400 25.4 3 BLU-113 368.3 1 996 3 886 58.0 3 BLU-122 389.0 2 018 4 038 44.5 WDU-43B 234.0 454 2 400 41.5 9 SDB 150.0 129 1 800 10.8 3
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